Wesay the data iselectrovacuumifμM= 0 andj= 0.

Theξibe one of the Killing vectors that generate the groupSO(3), then we say thethe initial data set isspherically symmetricif£ξhij=£ξKij=£ξμ=£ξji= 0,(100)for all the generatorsξofSO(3),

we restrict ourselves to spherically symmetric initial data where the3-dimensional Riemannian manifold is taken to beR3. We call themreg-ular spherically symmetricinitial data. We also assume that the data areasymptotically flat.